%I #21 Jun 20 2018 01:32:41

%S 1,2,2,3,3,4,4,4,4,5,5,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,10,

%T 10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,

%U 13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15

%N a(n) = the number k such that s(k)=0 where s(0)=n and s(i)=s(i-1)-(s(i-1) modulo i).

%C a(n+1) = number of Mancala numbers <= n, see A007952; n occurs A028913(n-1) times consecutively. - _Reinhard Zumkeller_, Jun 21 2008

%C a(n) = number of ones <= n in A130747; see also A002491. - _Reinhard Zumkeller_, Jul 01 2009

%H R. Zumkeller, <a href="/A082447/b082447.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: a(n) = sqrt(Pi*n) + O(1)

%F a(n) = A073047(n) - 1.

%e If n=6 : s(0)=6, s(1)=6-6 mod 2=6, s(2)=6-6 mod 3=6, s(3)=6-6 mod 4=6-2=4, s(4)=4-4 mod 5=0, hence a(6)=4.

%e If s(0)=4, 4 ->4-4 mod 1=4 ->4-4 mod 2=4 ->4-4 mod 3=3 ->3-3 mod 4=0, hence s(4)=0 and a(4)=4.

%t Flatten@Table[First@Position[Rest@FoldList[#1-Mod[#1,#2]&,i,Range[2,i+1]],0], {i,30}] (* _Birkas Gyorgy_, Feb 26 2011 *)

%o (PARI) a(n)=if(n<1,0,s=n; c=1; while(s-s%c>0,s=s-s%c; c++); c)

%Y Cf. A140060, A140061.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 25 2003